Geodesic
Measure of noncompactness of linear operators between spaces of sequences that are $(\bar{N},q)$ summable or bounded
Czechoslovak Mathematical Journal, Tome 51 (2001) no. 3, pp. 505-522 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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In this paper we investigate linear operators between arbitrary BK spaces $X$ and spaces $Y$ of sequences that are $(\bar{N},q)$ summable or bounded. We give necessary and sufficient conditions for infinite matrices $A$ to map $X$ into $Y$. Further, the Hausdorff measure of noncompactness is applied to give necessary and sufficient conditions for $A$ to be a compact operator.
In this paper we investigate linear operators between arbitrary BK spaces $X$ and spaces $Y$ of sequences that are $(\bar{N},q)$ summable or bounded. We give necessary and sufficient conditions for infinite matrices $A$ to map $X$ into $Y$. Further, the Hausdorff measure of noncompactness is applied to give necessary and sufficient conditions for $A$ to be a compact operator.
Classification : 40H05, 46A45, 47B07, 47B37
Keywords: BK spaces; bases; matrix transformations; measure of noncompactness 
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     title = {Measure of noncompactness of linear operators between spaces of sequences that are $(\bar{N},q)$ summable or bounded},
     journal = {Czechoslovak Mathematical Journal},
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Malkowsky, E.; Rakočević, V. Measure of noncompactness of linear operators between spaces of sequences that are $(\bar{N},q)$ summable or bounded. Czechoslovak Mathematical Journal, Tome 51 (2001) no. 3, pp. 505-522. http://geodesic.mathdoc.fr/item/CMJ_2001_51_3_a5/

[1] R. R. Akhmerov, M. I. Kamenskii, A. S. Potapov, A. E. Rodkina and B. N. Sadovskii: Measures of noncompactness and condensing operators. Oper. Theory Adv. Appl. 55 (1992), Birkhäuser Verlag, Basel. | DOI | MR

[2] A. M. Aljarrah and E. Malkowsky: BK spaces, bases and linear operators. Suppl. Rend. Circ. Mat. Palermo (2) 52 (1998), 177–191. | MR

[3] J. Banás and K. Goebl: Measures of noncompactness in Banach spaces. Lecture Notes in Pure and Appl. Math. 60 (1980), Marcel Dekker, New York and Basel. | MR

[4] G. H. Hardy: Divergent Series. Oxford University Press, 1973. | MR

[5] E. Malkowsky: Linear operators in certain BK spaces. Bolyai Soc. Math. Stud. 5 (1996), 259–273. | MR | Zbl

[6] E. Malkowsky and S. D. Parashar: Matrix transformations in spaces of bounded and convergent difference sequences of order $m$. Analysis 17 (1997), 87–97. | DOI | MR

[7] E. Malkowsky and V. Rakočević: The measure of noncompactness of linear operators between certain sequence spaces. Acta Sci. Math. (Szeged) 64 (1998), 151–170. | MR

[8] E. Malkowsky and V. Rakočević: The measure of noncompactness of linear operators between spaces of $m^{th}$-order difference sequences. Studia Sci. Math. Hungar. 35 (1999), 381–395. | MR

[9] V. Rakočević: Funkcionalna analiza. Naučna knjiga. Beograd, 1994.

[10] A. Wilansky: Summability through functional analysis. North-Holland Math. Stud. 85 (1984). | MR | Zbl